Synchronization of Kuramoto oscillators with the distributed time-delays and inertia effect

References

• Kuramoto Y. Self-entrainment of a population of coupled non-linear oscillators. In: International Symposium on Mathematical Problems in Theoretical Physics; New York. Springer; 1975. pp. 420–422. (Lecture Notes in Phys. 39).
   Google Scholar
• Kuramoto Y. Chemical oscillations waves and turbulence. Berlin: Springer; 1984.
   Google Scholar
• Acebròn JA, Bonilla LL, Prez CJ, et al. The Kuramoto model: a simple paradigm for synchronization phenomena. Rev Mod Phys. 77:137–185.
   Web of Science ®Google Scholar
• Dörfler F, Bullo F. Synchronization in complex networks of phase oscillators: a survey. Automatica. 2014;50(6):1539–1564.
   Web of Science ®Google Scholar
• Ermentrout B. Synchronization in a pool of mutually coupled oscillators with random frequencies. J Math Biol. 1985;22:1–9.
   Web of Science ®Google Scholar
• Ermentrout B. An adaptive model for synchrony in the firefly Pteroptyx malaccae. J Math Biol. 1991;29:571–585.
   Web of Science ®Google Scholar
• van Hemmen JL, Wreszinski WF. Lyapunov function for the Kuramoto model of nonlinearly coupled oscillators. J Stat Phys. 1993;72:145–166.
   Web of Science ®Google Scholar
• Strogatz SH. From Kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D. 2000;143(1–4):1–20.
   Web of Science ®Google Scholar
• Benedetto D, Caglioti E, Montemagno U. On the complete phase synchronization for the Kuramoto model in the mean-field limit. Commun Math Sci. 2015;13(7):1775–1786.
   Web of Science ®Google Scholar
• Choi Y-P, Ha S-Y, Jung S, et al. Asymptotic formation and orbital stability of phase-locked states for the Kuramoto model. Physica D. 2012;241:735–754.
   Web of Science ®Google Scholar
• Dörfler F, Bullo F. On the critical coupling for Kuramoto oscillators. SIAM J Appl Dyn Syst. 2011;10(3):1070–1099.
   Web of Science ®Google Scholar
• Ha S-Y, Kim H, Park J. Remarks on the complete frequency synchronization of Kuramoto oscillators. Nonlinearity. 2015;28:1441–1462.
   Web of Science ®Google Scholar
• Ha S-Y, Kim Y, Li Z. Large-time dynamics of Kuramoto oscillators under the effects of inertia and frustration. SIAM J Appl Dyn Sys. 13(1):466–492.
   Web of Science ®Google Scholar
• Hsia C-H, Jung C-Y, Kwon B. On the synchronization theory of Kuramoto oscillators under the effect of inertia. J Differ Equ. 2019;267(2):742–775.
   Web of Science ®Google Scholar
• Atay F.M. The consensus problem in networks with transmission delays. Philos Trans R Soc Lond Ser A Math Phys Eng Sci. 2013;371(1999):Article ID 20120460, 13 pp.
   Google Scholar
• Lohe MA. Synchronization control in networks with uniform and distributed phase lag. Automatica J IFAC. 2015;54:114–123.
   Web of Science ®Google Scholar
• Tseng J-P. A novel approach to synchronization of nonlinearly coupled network systems with delays. Physica A. 2016;452(15):266–280.
   Web of Science ®Google Scholar
• Tseng J-P. Global cluster synchronization in nonlinearly coupled community networks with heterogeneous coupling delays. Neural Netw. 2017;86:18–31.
   PubMed Web of Science ®Google Scholar
• Acebron JA, Bonilla LL, DeLeo S, et al. Time delay in the Kuramoto model with bimodal frequency distribution. Phys Rev E. 1998;57:5287.
   Web of Science ®Google Scholar
• Montbrio E, Kurths J, Blasius B. Synchronization of two interacting populations of oscillators. Phys Rev E. 2004;70:Article ID 056125.
   Web of Science ®Google Scholar
• Niebur E, Schuster HG, Kammen DM. Phys Rev Lett. 1991;67:2753.
   PubMed Web of Science ®Google Scholar
• Yeung MKS, Strogatz SH. Time delay in the Kuramoto model of coupled oscillators. Phys Rev Lett. 1999;82:648–651.
   Web of Science ®Google Scholar
• Schuster P. Wagner HG. Mutual entrainment of two limit cycle oscillators with time delayed coupling. Prog Theor Phys. 1989;81(5):939–945.
   Google Scholar
• Choi MY, Kim HJ, Kim D, et al. Synchronization in a system of globally coupled oscillators with time delay. Phys Rev E. 2000;61:371–381.
   Web of Science ®Google Scholar
• Kim S, Park SH, Ryu CS. Multistability in coupled oscillator systems with time delay. Phys Rev Lett. 1997;79:2911.
   Web of Science ®Google Scholar
• Montbrio E, Pazo D, Schmidt J. Time delay in the Kuramoto model with bimodal frequency distribution. Phys Rev E. 2006;74:Article ID 056201.
   Web of Science ®Google Scholar
• Lee WS, Ott E, Antonsen TM. Large coupled oscillator systems with heterogeneous interaction delays. Phys Rev Lett. 2009;103:Article ID 044101.
   Web of Science ®Google Scholar
• Hsia C-H, Jung C-Y, Kwon B, et al. Synchronization of Kuramoto oscillators with time-delayed interactions and phase lag effect. J Differ Equ. 2020;268(12):7897–7939.
   Web of Science ®Google Scholar
• Goldobin DS, Teramae J-n., Nakao H, et al. Dynamics of limit-cycle oscillators subject to general noise. Phys Rev Lett. 2010;105:Article ID 154101.
   PubMed Web of Science ®Google Scholar
• Teramae J-n., Nakao H, Ermentrout G.B.. Stochastic phase reduction for a general class of noisy limit cycle oscillators. Phys Rev Lett. 2009;102:Article ID 194102.
   PubMed Web of Science ®Google Scholar
• Teramae J-n., Tanaka D. Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators. Phys Rev Lett. 2004;93(20).
   PubMed Web of Science ®Google Scholar
• Ben-Khalifa N, El-Azouzi R, Hayel Y. Discrete and continuous distributed delays in replicator dynamics. Dyn Games Appl. Dec 2018;8(4):713–732.
   Web of Science ®Google Scholar
• Cooke KL, Grossman Z. Discrete delay distributed delay and stability switches. J Math Anal Appl. 1982;86(2):592–627.
   Web of Science ®Google Scholar
• Rahman B, Blyuss KB, Kyrychko YN. Dynamics of neural systems with discrete and distributed time delays. SIAM J Appl Dyn Sys. 2015;14(4):2069–2095.
   Web of Science ®Google Scholar
• Hsia C-H, Jung C-Y, Kwon B, et al. Synchronization of Kuramoto–Sakaguchi model with the distributed time-delayed interactions, preprint; 2020.
   Google Scholar
• Skardal PS. Stability diagram, hysteresis, and critical time delay and frequency for the Kuramoto model with heterogeneous interaction delays, preprint. Available from: https://arxiv.org/pdf/1707.02249.pdf
   Google Scholar